Biomedical subjects
Publications and source records attributed to J. D. Meiss.
Several families of volume-preserving maps on R(3) that have an integral are constructed using techniques due to Suris. We study the dynamics of these maps as the topology of the two-dimensional level sets of the invariant changes. (c) 2002 American Institute of Physics.
For a volume-preserving map, we show that the exit time averaged over the entry set of a region is given by the ratio of the measure of the accessible subset of the region to that of the entry set. This result is primarily of interest to show two things: First, it gives a simple bound on the algebraic decay exponent of the survival probability. Second, it gives a tool for computing the measure of the accessible set. We use this to compute the measure of the bounded orbits for the Henon quadratic map. (c) 1997 American Institute of Physics.
The exit time decomposition of a set yields a description of the transport through the set as well as a visualization of the invariant structures inside it. We construct several sets computationally easier to deal with than the construction of resonances, based on the ordering properties for orbits of twist maps. Furthermore these sets can be constructed for four- and higher-dimensional twist mappings. For the four-dimensional case-using the example of Froeshle-we find "practically" invariant volumes surrounding elliptic fixed points. The boundaries of these regions are remarkably sharp; however, the regions are threaded by "tubes" of escaping orbits.
Although almost all orbits in the stadium billiard are "chaotic," there are many regular orbits as well-the ordered periodic orbits and cantori. The symmetries of the stadium are exploited to find maximizing and saddle periodic orbits. Cantori are maximizing quasiperiodic orbits; they have caustics. Transport in the stadium should be impeded by cantori, just as in any twist map; this is particularly important for those orbits that are nearly glancing.